It is absolutely not secure. Text messages function essentially the same way email does: your client (phone) forwards it to a server, which then looks up a destination which may be on another network (carrier) and then sends it over where it is held in a mailbox until a phone gets it.

Anywhere along the way it can be copied, retained longer than expected, etc. Lawful interception, unlawful interception, cloned phones, Google+ accounts, etc are all ways a message can end up somewhere unexpected and all that assumes you trust the phone and software on it.

Clear text is compromised text. Always.